- #1
kmarinas86
- 979
- 1
I know there is:
I would have thought the former and latter affect the notions of wavelength and frequency of light respectively, am I not right?
However, then we (the shruken and time-slowed) are left with a increase apparent wavelength of a distant photon by a factor of [itex]1/\sqrt{1-2GM/rc^2}[/itex] and a increase apparent frequency of a distant photon by a factor of [itex]1/\sqrt{1-2GM/rc^2}[/itex], resulting in a increase in the apparent speed of distant light by a factor of [itex]1/(1-2GM/rc^2)[/itex].
Then there is the coordinate speed of light which is reduced by the factor [itex]1-2GM/rc^2[/itex], where [itex]r[/itex] refers to the radius from the gravitating object where the light is considered.
But now we are stuck with another problem. We observers at [itex]r[/itex] will have a clock running a rate [itex]\sqrt{1-2GM/rc^2}[/itex] times as much than a distant observer not in orbit. But our coordinate speed of light at [itex]r[/itex] is [itex]1-2GM/rc^2[/itex] times as much-a larger difference! That would mean that the apparent speed of light for the distant observer would be [itex]1/\sqrt{1-2GM/rc^2}[/itex] times as much. ? Surely, I am understanding something wrong.
- A gravitational length contraction by the factor of [itex]\sqrt{1-2GM/rc^2}[/itex]
- A time slowing by the factor of [itex]\sqrt{1-2GM/rc^2}[/itex]
I would have thought the former and latter affect the notions of wavelength and frequency of light respectively, am I not right?
However, then we (the shruken and time-slowed) are left with a increase apparent wavelength of a distant photon by a factor of [itex]1/\sqrt{1-2GM/rc^2}[/itex] and a increase apparent frequency of a distant photon by a factor of [itex]1/\sqrt{1-2GM/rc^2}[/itex], resulting in a increase in the apparent speed of distant light by a factor of [itex]1/(1-2GM/rc^2)[/itex].
Then there is the coordinate speed of light which is reduced by the factor [itex]1-2GM/rc^2[/itex], where [itex]r[/itex] refers to the radius from the gravitating object where the light is considered.
But now we are stuck with another problem. We observers at [itex]r[/itex] will have a clock running a rate [itex]\sqrt{1-2GM/rc^2}[/itex] times as much than a distant observer not in orbit. But our coordinate speed of light at [itex]r[/itex] is [itex]1-2GM/rc^2[/itex] times as much-a larger difference! That would mean that the apparent speed of light for the distant observer would be [itex]1/\sqrt{1-2GM/rc^2}[/itex] times as much. ? Surely, I am understanding something wrong.